Moscow University Physics Bulletin

, Volume 62, Issue 1, pp 19–22 | Cite as

Calculation of the gas flow rate in a microchannel

  • T. G. Elizarova
  • D. G. Ershov


Approximation formulas are obtained for calculation of the gas flow rate in long isothermal microchannels. The quasi-gas-dynamic equations with Maxwell’s slip conditions are shown to predict a minimum in the flow rate within a channel that is called the Knudsen minimum. Corrections are proposed enabling derivation of approximate formulas for flow rates valid for any Knudsen number.


Knudsen Number Approximate Formula Channel Cross Section Cylindrical Channel Burnett Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Present, R.D., Kinetic Theory of Gases, New York, 1958.Google Scholar
  2. 2.
    Cercigniani, C., Theory and Application of the Boltzmann Equation, Edinburgh, 1975.Google Scholar
  3. 3.
    Cercigniani, C. and Sernagiotto, F., Phys. Fluids, 1966, vol. 9, no. 1, p. 40.CrossRefGoogle Scholar
  4. 4.
    Cercigniani, C., Lampis, M., and Lorenzani, S., Phys. Fluids, 2004, vol. 16, no. 9, p. 3426.CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Kun, Xu and Zhihui, Li, J. Fluid Mech., 2004, vol. 513, p. 87.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Elizarova, T.G. and Sheretov, Yu.V., Rev. Int. de l’Eau, 2003, no. 5, p. 66.Google Scholar
  7. 7.
    Sheretov, Yu.V., Primenenie funktsional’nogo analiza v teorii priblizhenii (Application of Functional Analysis in the Approximation Theory), Tver, 1997.Google Scholar
  8. 8.
    Sheretov, Yu.V., Matematicheskoe modelirovanie techenii zhidkosti i gaza na osnove kvazigidrodinamicheskikh and kvazigazodinamicheskikh uravneni (Mathematical Simulation of Fluid Flow on the Basis of Quasi-Hydrodynamic and Quasi-Gas-Dynamic Equations), Tver, 2000.Google Scholar
  9. 9.
    Elizarova, T.G., Matematcheskie modeli i chislennye metody v dinamike zhidkosti i gaza (Mathematical Models and Numerical Methods in Fluid Dynamics), parts 1 and 2, Moscow, 2005.Google Scholar
  10. 10.
    Landau, L.D. and Lifshitz, E.M., Gidrodinamika (Hydrodynamics), Moscow, 1986.Google Scholar
  11. 11.
    Abramovich, G.N., Prikladnaya gazovaya dinamika (Applied Gas Dynamics), Moscow, 1991.Google Scholar
  12. 12.
    Bird, G.A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford, 1994.Google Scholar

Copyright information

© Allerton Press, Inc. 2007

Authors and Affiliations

  • T. G. Elizarova
    • 1
  • D. G. Ershov
    • 2
  1. 1.Institute of Mathematical SimulationRussian Academy of SciencesMoscowRussia
  2. 2.Department of Mathematics, Faculty of PhysicsMoscow State UniversityLeninskie Gory, MoscowRussia

Personalised recommendations